Question

Suppose that f has a continuous second derivative for all x, and that f(0) = 1, f ' (0) = 2, and f''(0) = 0.
A. Does f have an inflection point at x = 0? Explain your answer.

B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g. Write the
equation of the tangent line to g at this point.

C. Use your tangent line to approximate g(0. 3).

D. Find g''(0).

Answer 1

I feel like A is no because f'(0) would have to = 0 for it to be a critical point? Is that correct?

Answer 2

no it can be an inflection point even if its not a critical point